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Show that Eq. 5.31 gives the value A = 2/L.
To complete the solution for (x),...
1) (35 points) The wave function for a particle moving along x axis between the limits 0 and L is: (x)-C sin (nx xL) where n are 1, 2, 3, A) Determine the normalization constant C B) Why can'...
1) (35 points) The wave function for a particle moving along x axis between the limits 0 and L is: (x)-C sin (nx xL) where n are 1, 2, 3, A) Determine the normalization constant C B) Why can't n take the value of 0, briefly explain C) For n-3 determine the values of x (in terms of L) that correspond to a maximum or a minimum in the wave function D) For n-3 determine the values of x (in...
Consider a particle encountering a barrier with potential U = U.>0 between x = -a and...
Consider a particle encountering a barrier with potential U = U.>0 between x = -a and x = a with incoming energy E > U. a) Write the symbolic wave functions before and after passing through the barrier (i.e., for x<-a and x>a; regions I and III). U1 b) Write down the Schrodinger equation for the wave function in the middle (region II) where the potential is non-zero i.e., where -a<x<a; region II). c) What solution would you try for...
1. The wave-functions of the states [4) and (0) are given by y(x) and Q(x), respectively....
1. The wave-functions of the states [4) and (0) are given by y(x) and Q(x), respectively. Derive the expression for the inner product (14) in terms of the wave- functions Q(x) and (x). What is the physical meaning of y(x) and (x)/2? 2. Fig. 1 shows a sketch of y(x). Sketch y(x) such that the states (4) and (o) are orthogonal: (014) = 0. (x) M Figure 1 3. Assume a particle has a wave-function y(x) sketched in Fig. 2....
1. The wave-functions of the states [4) and (0) are given by y(x) and Q(x), respectively....
1. The wave-functions of the states [4) and (0) are given by y(x) and Q(x), respectively. Derive the expression for the inner product (14) in terms of the wave- functions Q(x) and (x). What is the physical meaning of y(x) and (x)/2? 2. Fig. 1 shows a sketch of y(x). Sketch y(x) such that the states (4) and (o) are orthogonal: (014) = 0. (x) M Figure 1 3. Assume a particle has a wave-function y(x) sketched in Fig. 2....
a) The wave-functions of the states [) and (o) are given by y(x) and (x), respectively....
a) The wave-functions of the states [) and (o) are given by y(x) and (x), respectively. Derive the expression for the inner product (4) in terms of the wave- functions Q(x) and (x). What is the physical meaning of y(x) and (x)/2? b) Fig. 1 shows a sketch of y(x). Sketch y(x) such that the states [4) and (o) are orthogonal: (14) = 0. (x) M Figure 1 c) Assume a particle has a wave-function y(x) sketched in Fig. 2....
A NON stationary state A particle of mass m is in an infinite square well potential of width L, a...
A NON stationary state A particle of mass m is in an infinite square well potential of width L, as in McIntyre's section 5.4. Suppose we have an initial state vector lv(t -0) results from Mclntrye without re-deriving them, and you may use a computer for your math as long as you include your code in your solution A(3E1) 4iE2)). You may use E. (4 pts) Use a computer to plot this probability density at 4 times: t 0, t2...
Consider in x [0, L], the second order Boundary Value Problem lu where qra+bx. The solution is su...
Consider in x [0, L], the second order Boundary Value Problem lu where qra+bx. The solution is subject to the boundary conditions du dxl Find an approximate solution using the using a three-node element. The shape function of the element is, in a local coordinate system s E[, Thus local node number 1 is to the left (s--1) and number 2 is in centre (s -0) and the third node is to the right (s 1) Hint: Assume that the...
need help with this problem. please explain, thank you. 8. Consider a particle encountering a barrier...
need help with this problem. please explain, thank you.
8. Consider a particle encountering a barrier with potential U = U, >0 between x = -a and x = a with incoming energy E > U. a) Write the symbolic wave functions before and after passing through the barrier (i.e., for xs-a and x>a; regions I and III). UN b) Write down the Schrodinger equation for the wave function in the middle (region II) where the potential is non-zero i.e.,...
Using equation 3 please find the deflection value with the variables given. Be careful with units...
Using equation 3 please find the deflection value with the
variables given. Be careful with units please.
P= 10.07 Newtons
L= 953.35 mm
x= 868.363 mm
E= 72.4 GPa
Iy= 5926.62 mm^4
The maximum deflection, WMAX of the cantilever beam occurs at the free end. The magnitude of the deflection may be derived by solving the differential equation: d'w M,(x) P (L-x) eq. 1 dr EI EI where E and Iy are the modulus of elasticity and moment of inertia...
Extra Credit (3 points to Mideterm-2) Q1. A particle is described by the wave function (x)...
Extra Credit (3 points to Mideterm-2) Q1. A particle is described by the wave function (x) b(a2-x2) for -a sx s a and (x) 0 for x -a and x +a, where a and b are positive real constants. (a) Using the normalization condition, find b in terms a. (b) What is the probability to find the particle at x = +a/2 in a small interval ofwidth 0.01 a ? (c) What is the probability for the particle to be...
1) (35 points) The wave function for a particle moving along x axis between the limits 0 and L is: (x)-C sin (nx xL) where n are 1, 2, 3, A) Determine the normalization constant C B) Why can't n take the value of 0, briefly explain C) For n-3 determine the values of x (in terms of L) that correspond to a maximum or a minimum in the wave function D) For n-3 determine the values of x (in...
Consider a particle encountering a barrier with potential U = U.>0 between x = -a and x = a with incoming energy E > U. a) Write the symbolic wave functions before and after passing through the barrier (i.e., for x<-a and x>a; regions I and III). U1 b) Write down the Schrodinger equation for the wave function in the middle (region II) where the potential is non-zero i.e., where -a<x<a; region II). c) What solution would you try for...
1. The wave-functions of the states [4) and (0) are given by y(x) and Q(x), respectively. Derive the expression for the inner product (14) in terms of the wave- functions Q(x) and (x). What is the physical meaning of y(x) and (x)/2? 2. Fig. 1 shows a sketch of y(x). Sketch y(x) such that the states (4) and (o) are orthogonal: (014) = 0. (x) M Figure 1 3. Assume a particle has a wave-function y(x) sketched in Fig. 2....
1. The wave-functions of the states [4) and (0) are given by y(x) and Q(x), respectively. Derive the expression for the inner product (14) in terms of the wave- functions Q(x) and (x). What is the physical meaning of y(x) and (x)/2? 2. Fig. 1 shows a sketch of y(x). Sketch y(x) such that the states (4) and (o) are orthogonal: (014) = 0. (x) M Figure 1 3. Assume a particle has a wave-function y(x) sketched in Fig. 2....
a) The wave-functions of the states [) and (o) are given by y(x) and (x), respectively. Derive the expression for the inner product (4) in terms of the wave- functions Q(x) and (x). What is the physical meaning of y(x) and (x)/2? b) Fig. 1 shows a sketch of y(x). Sketch y(x) such that the states [4) and (o) are orthogonal: (14) = 0. (x) M Figure 1 c) Assume a particle has a wave-function y(x) sketched in Fig. 2....
A NON stationary state A particle of mass m is in an infinite square well potential of width L, as in McIntyre's section 5.4. Suppose we have an initial state vector lv(t -0) results from Mclntrye without re-deriving them, and you may use a computer for your math as long as you include your code in your solution A(3E1) 4iE2)). You may use E. (4 pts) Use a computer to plot this probability density at 4 times: t 0, t2...
Consider in x [0, L], the second order Boundary Value Problem lu where qra+bx. The solution is subject to the boundary conditions du dxl Find an approximate solution using the using a three-node element. The shape function of the element is, in a local coordinate system s E[, Thus local node number 1 is to the left (s--1) and number 2 is in centre (s -0) and the third node is to the right (s 1) Hint: Assume that the...
need help with this problem. please explain, thank you.
8. Consider a particle encountering a barrier with potential U = U, >0 between x = -a and x = a with incoming energy E > U. a) Write the symbolic wave functions before and after passing through the barrier (i.e., for xs-a and x>a; regions I and III). UN b) Write down the Schrodinger equation for the wave function in the middle (region II) where the potential is non-zero i.e.,...
Using equation 3 please find the deflection value with the
variables given. Be careful with units please.
P= 10.07 Newtons
L= 953.35 mm
x= 868.363 mm
E= 72.4 GPa
Iy= 5926.62 mm^4
The maximum deflection, WMAX of the cantilever beam occurs at the free end. The magnitude of the deflection may be derived by solving the differential equation: d'w M,(x) P (L-x) eq. 1 dr EI EI where E and Iy are the modulus of elasticity and moment of inertia...
Extra Credit (3 points to Mideterm-2) Q1. A particle is described by the wave function (x) b(a2-x2) for -a sx s a and (x) 0 for x -a and x +a, where a and b are positive real constants. (a) Using the normalization condition, find b in terms a. (b) What is the probability to find the particle at x = +a/2 in a small interval ofwidth 0.01 a ? (c) What is the probability for the particle to be...
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